January 20 is the day that the United States Constitution mandates that the old president complete his term, and the new president should begin his term. Not only that, but this has to occur at 12 noon. It's quite a feat of organization to ensure that this event occur exactly on that day exactly at that time, in order to be Constitutional.
The term of the new president used to begin on March 4, but the Amendment XX, adopted on Jan. 23, 1933, moved that date to January 20.
He becomes president by taking an Oath (or Affirmation) of Office, which begins, "I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States."
Here we see the verb, (to) swear. This means he makes a solemn promise. Notice it says "I... swear.... that...." and then we read what the person swears, or pledges, or affirms.
The two-word verb, (to) swear in, is different. It's always transitive and it's usually used in the PASSIVE VOICE.
Donald Trump Is Sworn In as PresidentNotice what follows this verb: as and the name of the office that he now legally and constitutionally assumes.
Vice President Mike Pence sworn in
As is typical in journalism and advertising captions, the "be" verb is omitted. Immediately following the caption, we see the sentence,Indiana Gov. Mike Pence is sworn in as Vice President of the United States.
Then there's the NOUN FORM, a swearing-in.
Donald Trump inauguration: protesters march following swearing-in
... and also the ADJECTIVE FORM: swearing-in:
The President's Swearing-In Ceremony
If we are ever in a court case and have to testify, we are sworn in - that is, we affirm that we will be telling the truth. But to be sworn into office is a very unusual thing.
Here is a photo of William Renquist being sworn in as Justice of the United States Supreme Court:
It's pretty amazing to think that with just 35 words, a person can be sworn in and assume the title of President of the United States. We always hope that the person upholds his oath.